Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27161892 | C2 | semidirect |
| 2. #27161888 | C2 | semidirect |
| 3. #27161884 | C2 | semidirect |
| 4. #27161464 | C2 | semidirect |
| 5. #27161350 | C2 | semidirect |
| 6. #27161345 | C2 | semidirect |
| 7. #27161255 | C2 | semidirect |
| 8. #27161254 | C2 | semidirect |
| 9. #27161195 | C2 | semidirect |
| 10. #27161194 | C2 | semidirect |
| 11. #473×C197 | C2 | semidirect |
| 12. #20263374 | C22 | semidirect |
| 16. #20263357 | C22 | semidirect |
| 19. #20263354 | C22 | semidirect |
| 27. C2×#15691345 | C22 | semidirect |
| 31. #20263334 | C22 | semidirect |
| 32. #20263332 | C22 | semidirect |
| 33. #20263315 | C22 | semidirect |
| 34. #20263261 | C22 | semidirect |
| 36. #20263252 | C22 | semidirect |
| 37. #20263252 | C22 | semidirect |
| 38. #20263242 | C22 | semidirect |
| 39. C8×Dic197 | C22 | semidirect |
| 41. C2×Q16×C197 | C22 | semidirect |
| 43. #108×C197 | C22 | semidirect |
| 44. #101×C197 | C22 | semidirect |
| 149. C197 | #3290 | semidirect |
| 155. #473 | D197 | semidirect |
| 178. C2×Q16 | C2×D197 | semidirect |
| 188. #108 | C2×D197 | semidirect |
| 192. #101 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161892 | 2 |
| #27161888 | 2 |
| #27161884 | 2 |
| #27161464 | 2 |
| #27161350 | 2 |
| #27161345 | 2 |
| #27161255 | 2 |
| #27161254 | 2 |
| #27161195 | 2 |
| #27161194 | 2 |
| #473×C197 | 2 |
| #3290 | 197 |